Part $3$: Root Finding $(3$ pts$)$

Consider the equation $x^4+e^x-2=0$

a$)$ Discuss the applicability of Newtons method at initial estimate $x0=1\mathrm{.}5.$

b$)$ By using the result of question $($a$)$ write a program that finds an approximate of the root of the equation with an absolute error less than ${10}^{-4},$ checking the error after each iteration and provide the results of calculations as a table.